The grooves in a compact disc are very close together. One side of a disc
can hold more music than two sides of a vinyl record.

Just how close* are* the grooves? We can use a laser to find out.

When a beam of light reflects from the "groovy" surface of a CD,
a* diffraction pattern* is produced. To those who know how to analyze
it, this pattern *reveals* the distance between the grooves. [A diagram
of the arrangement is shown below.]

Fortunately, *we* know how to analyze the pattern.

The equation for the groove separation distance* d* may appear intimidating
at first:

*d* = *n*(*Lambda*)/sin(*Theta*)

where *n* is the **order** of the bright spot in the pattern, *Lambda*
is the **wavelength** of light reflecting from the CD to produce the
diffraction pattern, and *Theta* is the **angle** of orientation
of the bright spot. This angle is determined by measuring the distance*
x* from the CD to the "screen" (in this case, the mounted meterstick)
and the distance* y* of the first or second order bright spot from
the central (zero order) bright spot.

A bit of clever trigonometry turns *x* and *y* into an angle *Theta*.
Specifically,

*Theta* = Arctan(*y*/*x*)

The *arctangent* function is available on all scientific calculators.

So by knowing the wavelength of our laser light-632.8nm for the helium-neon
laser we are using-and by measuring the distances *x* and *y*,
we are able to determine the distance between the grooves on a compact disc.

What *is* that distance? Make the *x* and *y* measurements
yourself and the demonstrator will be happy to carry out the calculations
for you. [The actual distance of 1.6 micrometers is typically found to within
one or two percent error.]

Demonstration set-up and notes by Dean Baird, Rio Americano High School (San Juan Unified School District), Sacramento, CA.

Based on "The compact disc as a diffraction grating" by Haym Kruglak, Western Michigan University, Kalamazoo, MI as published in

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Comments? Suggestions? Rants? Raves? E-mail me at dbaird@jps.net

Copyright 1996 by Dean Baird. All rights reserved